KNOWING IS NOT UNDERSTANDING

There is a big difference between knowing a thing and understanding it. Suppose that young Jenny had been absent when the teacher taught “areas of triangles”. The teacher quickly tells young Jenny that you multiply the base and the height and then divide by 2. Jenny instantly gets the idea and confidently uses: Area = b × h 2and manages to use this formula correctly for next 10 questions. Young Jenny “knows” how to find the area of a triangle but she has no “understanding” of WHY the method works. To illustrate this point further, suppose she were told that the area of a triangle is found by multiplying the base and the height then dividing by 3. Area = b × h 3 Jenny would have cheerfully followed this formula and used it correctly for the next 10 questions believing that she “understands” how to find the area of a triangle. The fact that it produced wrong answers is irrelevant.KNOWING something is not the same as UNDERSTANDING it.Very often, teachers carefully go through the proper reasoning for some concept and yet a large proportion of students simply wait until the “formula” appears then simply apply the formula without understanding where it came from, despite the teacher’s best intentions. I believe students need to appreciate the logic in mathematics otherwise they are just following “rules”. Some people actually believe that mathematics is just a whole lot of rules and if you know the rules, you will be good at mathematics! Mathematics is completely logical and if you follow the logic it is enjoyable, exciting and very satisfying. Teachers should not be just emphasising the use of formulae such as: Area of a rectangle = b×h Area of a parallelogram = b×h Area of a triangle = b×h 2and by the way NEVER (½ base) × (height)!

CLICK ON THE FOLLOWING TOPICS TO DOWNLOAD IDEAS AND TEACHING METHODS WHICH FOCUS ON UNDERSTANDING AND NOT JUST RULES:

23. A simple Order of Operations problem is causing a lot of controversy on the internet. Click HERE to see this problem.

24. There are many ways to introduce INTEGERS to young students. After 47 years of teaching experience, I consider this to be by far the best way. Click HERE.​25. Question from the QUORA website: What is the order of transformations in graphs? Click HERE for my explanation.

26. Finding the equation of a tangent to a curve from a point NOT on the curve.​ Click HERE